5 ms·
Step-by-Step Math
- ludwig 17y agoIt would be also be nice if the list of steps wasn't displayed all at once, but more like a lazy evaluator (Show-Me-Next-Step?). That way you can let Mathematica lead you for a bit, but then still be able to proceed on your own without too much guidance. Then again, knowing the answer ahead of time doesn't really hurt since understanding the steps in between is what matters.
- yummyfajitas 17y agoSuffice it to say, my students love this. Graded homework is now obsolete. Of course, the department says graded homework must still be turned in...
- timwiseman 17y agoThere have always been ways to cheat at basic school work, if nothing else by grabbing someone who did know how to do it and copying theirs. This does add one more way, but it can also be constructive if struggling to learn something.
- amichail 17y agoGive homework where the most interesting part is not something that Wolfram Alpha can solve.
- dagw 17y agoI remember university teacher of mine had a collection of a few problems which if you typed it into Mathematica would give an answer on a very different form than what you would be likely to get if you solved by hand the 'normal' way. Handy for giving you a heads up on who might be 'cheating'.
- roundsquare 17y agoSame is true here. Look at the solution to the quadratic in the beginning. I suspect most students would use the quadratic formula and not complete the square by hand.
- DougBTX 17y agoAssume learning by doing, and Alpha's ability to solve any introductory problem, and you are screwed.
- pmichaud 17y agoI've been offering these kind of calculators for a while to students... but the department doesn't require a grad their homework. Is this college? What college department requires that sort of thing?
- yummyfajitas 17y agoIt is a college: http://www.math.nyu.edu/courses/Calculus/2009/Fall/122/hw.html http://www.math.nyu.edu/courses/Calculus/2009/Fall/122/hw.ht...
- kingkawn 17y agoYou'll be able to tell who those kids are because they'll die on the exam.
- pwmanagerdied 17y agoAs a personal exercise, I've been working on a basic math engine of my own recently. It's not very difficult to break problems down into computer-friendly steps, but if you approach them that way it's another challenge to choose the steps you should pull out to show in human-friendly output. Here's a screenshot of the output from a very simple example in the current version: http://imgur.com/hevar.png http://imgur.com/hevar.png. It uses LaTeX for the equations and Flot for the graphs. It's a fun project to work on; it can be surprising how far a program can get by just repeatedly applying some simple rules. :)
- tudorachim 17y agoAww, after I saw the integration examples I got my hopes up for a Show Steps for this... http://www.wolframalpha.com/input/?i=integrate%5Bexp%28-t%28t+a%5E2-u+b%5E2%2Bt+b%5E2%29%2F%28a%5E2+b%5E2%29%29%2C+t%5D http://www.wolframalpha.com/input/?i=integrate%5Bexp%28-t%28...
- wtallis 17y agoNoScript filters that link as a potential XSS attack. I guess it doesn't like brackets in URLs. That could be a problem for Wolfram if the noscript author can't find a safe way to whitelist wolfram alpha links.
- redorb 17y agoon a limb: I would say the overlap of no-script to wolframalpha users is minimal / WolframAlpha has other bigger problems to fix first.
- atamyrat 17y agoHow is that noscript strips URLs with brackets is WolframAlpha's problem?
- redorb 17y agomy point exactly / sorry for confusion.
- wtallis 17y agoMathematica (and thus Wolfram Alpha) is unusual in it's use of brackets to enclose function arguments. Every other computer algebra system I've used has been content with parentheses. And NoScript is pretty much the leading edge for browser security, so if it thinks brackets are dangerous, they probably are and other browsers could follow at any time. Wolfram Alpha's direct use of Mathematica's notation in URLs seems a bit naive, and it wouldn't be the first time Wolfram embarrassingly misunderstood the way the web works.
- pragmatic 17y agoWhere was this when I was working through Calculus 2... Kids have it easy these days. Seriously, this is really cool.
- andreshb 17y agoAgreed, easily one of the most exciting things Ive seen recently.
- Adrenalist 17y agoPriceless: This is pretty nice I would like to see the interface enhanced so I could enter several math problems at once (for example: Chapter 7, problems 1-19 (odd)) and have the output in a printable / customizable format (ie a script font that looks like my handwriting).
- deleted 17y ago[deleted]
- genieyclo 17y agoThis'll be perfect for precalc next semester
- andreshb 17y agoWhy oh why did you not exist when I was still in school! I was born too early...
- hh 17y agoI have been looking at sage (sagemath.org) and sympy to see if I can use open source math packages to do something like this for http://www.mathmaster.org http://www.mathmaster.org but I don't have any successes so far. Have you seen something like this besides commercial software? They have a nice API but looking at the licensing cost make me read no further.
- ntoshev 17y agoHmm, can I get Wolfram Alpha to compute a closed form solution of a recurrent sequence - like the Fibonacci numbers?
- bioweek 17y agoHow do you program something like that? I'm impressed.
- arohner 17y agoLet's treat this as an interview question: First, I'll assume alpha works similar to a compiler. It parses the text, and generates an AST for the input expression. Your goal is to replace the tree with the 'best' possible equivalent AST. Best here is a fitness function, that provides a score for a given AST. At first glance, we'll say the AST with the smallest number of nodes is optimal. Then, create a list of legal operations on a subtree. Try an operation, and see if the AST gets better. Repeat.
- mkyc 17y agoCheating is now easier. That's good, for two reasons: 1. The steps are small and have clear documentation. Copying a wall of numbers does nothing. Copying delimited steps while being told exactly what they are helps. Actually, it's a lot like typical classroom instruction! 2. Cheating from someone "smarter" allows rationalization. The class is hard, you suck at math, they're smart. But here a dumb process spits out answers. The typical response to this sort of narrow AI is "well, it's not that difficult after all". This suggests that you don't need an abundance of ingenuity to do rote math of this sort. And that's motivating, if you're feeling daft. The mediocre borrow and the great steal; if a novice learns from brute copying then we shouldn't give a damn.
- jrockway 17y agoI am so glad this didn't exist when I was taking calculus. I would have never learned anything :)
- orblivion 17y agoAren't they spreading themselves a little thin a little too early? Google can afford to explore different areas, but I think these guys should first work on an impressive engine for pulling together information on the web in a meaningful way before looking at more niche things like resolving math. Unless it somehow calls on the same AI base and was very little work to develop.